Archytas family

Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from 12edo and also a feature of 22edo and 27edo.

Comma: 64/63

7-limit minimax
[|1 0 0 0>, |2 1/3 0 -1/3>,
|2 -2/3 1 -1/3>, |2 -2/3 0 2/3>]
Eigenmonzos: 2, 6/5, 7/5

9-limit minimax
[|1 0 0 0>, |3/2 1/2 0 -1/4>,
|3/2 -1/2 1 -1/4>, |3 -1 0 1/2>]
Eigenmonzos: 2, 6/5, 9/7

Lattice basis: 3/2 length 1.0508 5/4 length 2.3219
Angle(3/2, 5/4) = 90 degrees
Map to lattice: [<0 1 0 -2|, <0 0 1 0|]

Map: [<1 0 0 6|, <0 1 0 -2|, <0 0 1 0|]
Generators: 2, 3, 5
Edos: 7, 10, 12, 15, 22, 27, 37, 49, 59
Scales: archytas12, archytas12synch

Music: Chris Vaisvil
12 archytas hobbits with ale
Joel Taylor
Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3

11 limit children

Ares

Commas: 64/63, 100/99

Minimax tuning
[|1 0 0 0 0>, |3/2 1/2 0 -1/4 0>,
|2 0 0 -1/2 1/2>, |3 -1 0 1/2 0>,
|3 -1 0 -1/2 1>]
Eigenmonzos: 2, 11/9, 9/7

Lattice basis: 3/2 0.9878 6/5 1.4312
Angle(3/2, 6/5) = 75.0475 degrees
Map to lattice: [<0 1 1 -2 0|, <0 0 -1 0 -2|]

Map: [<1 0 0 6 2|, <0 1 0 -2 -2|, <0 0 1 0 2|]
Generators: 2, 3, 5
Edos: 12, 15, 22, 37, 49
Badness: 0.000469

Scales: ares12

Vulcan

Commas: 56/55, 64/63

Map: [<1 0 0 6 9|, <0 1 0 -2 -2|, <0 0 1 0 -1|]
Generators: 2, 3, 5
EDOs: 5, 10, 12, 15
Badness: 0.000577